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A Bayesian Topological Data Analytic Approach to Classification of Handwritten Digits
August 13, 2025
We adopt t-distributed Stochastic Neighbor Embedding(t-SNE) to represent the data in 2D.(see details )
We use feedforward neural network which has the following structure
Multinomial logistic regression is equivalent to a NN with just input and output layers. There are no hidden layers.
Let’s train the network for 30 epochs, using a default batch size of 32. This means that images from the training set will be presented to the network in batches of 32 at a time, and for each batch, the SGD algorithm will update the network’s weights by an appropriate amount. Then another batch of 32 images will be presented, and so on, until all 60,000 training images in the dataset have been processed, which constitutes one epoch of training. This entire cycle will be repeated for 30 epochs. As training proceeds, the network’s error (loss) on both the training and testing/validation sets will be shown on the left graph, and the accuracy on each of these sets will be shown on the right graph. The accuracy is simply the fraction of input images that the network classifies correctly. A classification is considered correct if the largest output value on the output layer corresponds to the target classification
| method | accuracy |
|---|---|
| multinomial | 0.9855 |
| dropout nn | 0.9965 |
| ridge nn | 0.9948 |
| lasso no | 0.9948 |